• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.4
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• pp.58-65
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• 2005

A method measuring angular speed and estimating angular acceleration of an automotive wind shield wiper pivot with limited resources has been proposed. Limited resources refer to the fact that processes cannot be operated in real-time with a regular notebook running a Microsoft Windows. Also, they refer to the fact that data acquisition cards have only two general purpose counters as many generic cards do. An optical incremental encoder has been employed for measuring angular motion. To measure the angular speed of the pivot, periods for the encoder's output pulses have been measured as the speed is related to the reciprocal of the period. Since only information acquired from one counter channel is the magnitude of the angular speed, sign correction is necessary. Also the information for the exact time when a pivot passes left and right dead points is also missing and the situation is inherent to the hardware setup. To find out the zero-crossing time of the angular speed, a linear interpolation technique has been employed. Lastly, to overcome the imperfection of the mechanical encoders, the angular speed has been curve fitted to a spline. Angular acceleration can be obtained by a differentiation of the angular speed.

• Journal of Biomedical Engineering Research
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• v.30 no.2
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• pp.142-146
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• 2009

The purpose of this study is to investigate the angular velocity of forearm pronation/supination movement in Parkinson's disease patients, as a quantitative measure of the bradykinesia. Thirteen Parkinson's disease patients ($64{\pm}11.0$ yrs, male:6, female:7) participated in the experiments. The subjects' both right and left forearms were scored by a rater according to rapid alternating movement of hands category in the UPDRS (unified Parkinson's disease rating scale) and the angular velocity of forearm pronation/supination was measured at the same time. As analysis parameters, RMS (root mean square) angular velocity and RMS angle were used. The parameters showed negative correlation with the clinical score (RMS angular velocity: r= - 0.914, RMS angle: r= -0.749). The RMS angular velocity of all clinical scales were significantly different one another except for the non significant difference between those of scale 3 and 4. RMS angle of scale 0 was significantly different from those of scale 2, 3, 4 and that of scale 1 was significantly different from those of scale 3 and 4. This suggests that RMS angular velocity can be used for a quantitative measure of bradykinesia in motor examination.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.8
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• pp.29-36
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• 2008

An optical rotary encoder is easy to implement for automation system applications. In particular, the output of the encoder has a digital form pulse, which is also easy to be connected to a popular digital controller. By using an incremental encoder and a counting device, it is easy to measure angular displacement, as the number of the output pulses is proportional to the rotational displacement. This method can only detect the angular placement once a pulse signal comes out of the encoder. The angular displacement detection period is strongly subject to the change of the angular displacement in case of ultimate low velocity range. They have ultimate long detection period or cannot even detect angular displacement at near zero velocity. This paper proposes an algorithm for detecting angular displacement by using a dual encoder system with two encoders of normal resolution. The angular displacement detecting algorithm is able to keep detection period moderately at near zero velocity and even detect constant angular displacement within nominal period. It is useful for motion control applications in case of changing rotational direction at which there occurs zero velocity. In this paper, various experimental results are shown for the angular displacement detection algorithm.

• Journal of Positioning, Navigation, and Timing
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• v.8 no.3
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• pp.107-117
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• 2019

When a vehicle moves with a high rotation rate, it is not easy to measure the angular velocity using an off-the-shelf gyroscope. If the angular velocity is estimated using the extended Kalman filter in the gyro-free inertial navigation system, the effect of the accelerometer error and initial angular velocity error can be reduced. In this paper, in order to improve the navigation performance of the gyro-free inertial navigation system, an angular velocity estimation method is proposed based on an extended Kalman filter with an accelerometer random bias error model. In order to show the validity of the proposed estimation method, angular velocities and navigation outputs of a vehicle with 3 rev/s rotation rate are estimated. The results are compared with estimates by other methods such as the integration and an extended Kalman filter without an accelerometer random bias error model. The proposed method gives better estimation results than other methods.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.545-559
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• 2018

In this paper we mainly investigate the properties of the solutions to a type of nonhomogeneous algebraic differential equation in an angular domain. It includes the Borel directions of the solutions, the width of angular domains in which the solutions take its order and the measure of radial distributions of Julia sets of the solutions.

• Journal of Biosystems Engineering
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• v.14 no.4
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• pp.221-228
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• 1989

A data acquisition system was designed to measure the forces on a rolling coulter in three coordinated directions, angular velocity of the coulter and travel speed of a soil bin. The data acquisition system consisted of a dynamometer, speed transducers, a signal conditioner, an inter-face board, an Aim-65 microcomputer and a digital data recorder. Strain gages were attached on the surface of the dynamometer and connected to form three Wheatstone bridges, which measure the draft force, the vertical force and the side force on the coulter. An interaction among three dimensional forces was found during the calibration. A matrix procedure was used to correct the forces for this interaction. Rotary shaft encoders were mounted on the coulter and on the soil bin drive to measure the angular velocity of the coulter and the travel speed of the soil bin. The angular velocity and the travel speed were computed by counting the number of pulse signals from the rotary shaft encoders every 0.2 second. The digital signals from the rotary shaft encoders were connected to counters and the analog signals from the dynamometer, after passing through the signal conditioner, were connected to the A/D converter. The microcomputer programs, written in assembly language, were developed to read signals from the transducers, convert them to actual unit, display them upon request and record them on a sigital tape every 0.2 second.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1693-1696
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• 2003

In this paper, input-output velocity transmission characteristics of the Casing Oscillator, which is a constructional machine with 4 degree of freedom are examined. After the Jacobian matrix is decomposed into linear part and angular part, the linear and the angular velocity transmission characteristics are analyzed and visualized in easy way even in the case of 3 dimensional task space with 4 variables. Regarding the measure of dexterity of the Casing Oscillator, the kinematic isotropic index and the manipulability measures which are respectively represented the isotropy and the volume of the manipulability ellipsoid are combined. A performance of the Casing Oscillator is evaluated by the combined manipulability measure.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.904-914
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• 2004

In this paper, input-output velocity and force transmission characteristics of the Casing Oscillator which is a construction machine with 4 degrees of freedom are examined. After the Jacobian matrix is decomposed into the linear part and angular part, the velocity and force transmission characteristics for the linear and angular workspace are easily analyzed and visualized even if the Casing Oscillator has the spatial dimensional workspace with 4 DOF. Regarding the manipulability measure of the Casing Oscillator, the kinematic isotropic index and the manipulability measure which represent the isotropy and volume of the manipulability ellipsoid, respectively, are combined to coincidently consider them with respect to equivalent ranges and fluctuations. A performance of the Casing Oscillator is evaluated by the newly proposed manipulability measures.

• Journal of the Ergonomics Society of Korea
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• v.31 no.5
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• pp.647-655
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• 2012

Objective: The purpose of this study was to confirm difference between angular foot movement time and existing foot Fitts' law predicting times, and to develop the angular foot Fitts' law in the foot tapping task. Background: Existing studies of foot Fitts' law focused on horizontal movement to predict the movement time. However, when driving a car, humans move their foot from the accelerator to the brake with a fixed heel. Therefore, we examined the experiment to measure angular foot movement time in reciprocal foot tapping task and compared to conventional foot Fitts' law predicting time. And, we developed the angular foot Fitts' law. Method: In this study, we compared the angular foot movement time in foot tapping task and the predicted time of four conventional linear foot Fitts' law models - Drury's foot Fitts' law, Drury's ballistic, Hoffmann's ballistic, Hoffmann's visually-controlled. 11 subjects participated in this experiment to get a movement time and three target degrees of 20, 40, and 60 were used. And, conventional models were calculated for the prediction time. To analyze the movement time, linear and arc distance between targets were used for variables of model. Finally, the angular foot Fitts' law was developed from experimental data. Results: The average movement times for each experiment were 412.2ms, 474.9ms, and 526.6ms for the 89mm, 172mm, and 253mm linear distance conditions. The results also showed significant differences in performance time between different angle level. However, all of conventional linear foot Fitts' laws ranged 135.6ms to 401.2ms. On the other hand, the angular foot Fitts' law predicted the angular movement time well. Conclusion: Conventional linear foot Fitts' laws were underestimated and have a limitation to predict the foot movement time in the real task related angular foot movement. Application: This study is useful when considering the human behavior of angular foot movement such as driving or foot input device.